$\lambda$ - Constant Function Markets Generalizing and Mixing Automated Market Makers

Abstract

One of the most exciting recent developments in Decentralized Finance (DeFi) has been the development of decentralized exchanges, called Automated Market Mak-ers (AMMs). In this work, we study the most prominent special class of them, the Constant Function Market Makers (CFMMs). We introduce a generalized formula for CFMMs, called λCFMMs, which encapsulates the idea of combining the advantages of constant sum and constant mean CFMMs by blending their functions where$\lambda$is the degree of mixture. Our experiments demonstrate the behaviour of this generalized formula for various token pools with different properties and price differences, and evaluate its performance regarding slippage and imper-manent loss for different degrees of mixture during a trading period. We further show that given the nature of the pool and an optimization objective, different levels of mixture lead to optimal non-trivial functions, which as we show, outperform some of the most popular AMMs such as Uniswap. The novelty of$\lambda$CFMMs is both the mixing method that helps us target more efficient AMM functions and also the fact that motivates the idea of dynamic AMM functions that given certain features can self-adjust their parameters in order to produce mutual profits for both the traders and the liquidity providers.